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Original Articles

Small noise limit for diffusions near heteroclinic networks

Pages 413-431 | Received 13 Dec 2009, Accepted 30 Mar 2010, Published online: 07 May 2010

References

  • Bakhtin , Y . 2010 . Noisy heteroclinic networks . Probability Theory Rel. Fields , DOI: 10.1007/s00440-010-0264-0
  • Armbruster , D , Stone , E and Kirk , V . 2003 . Noisy heteroclinic networks . Chaos , 13 ( 1 ) : 71 – 86 .
  • Bakhtin , Y . 2008 . Exit asymptotics for small diffusion about an unstable equilibrium . Stochastic Process. Appl. , 118 ( 5 ) : 839 – 851 .
  • Kifer , Y . 1981 . The exit problem for small random perturbations of dynamical systems with a hyperbolic fixed point . Israel J. Math. , 40 ( 1 ) : 74 – 96 .
  • Krupa , M . 1997 . Robust heteroclinic cycles . J. Nonlinear Sci. , 7 ( 2 ) : 129 – 176 .
  • Øksendal , B . 1995 . Stochastic Differential Equations, , 4th , Berlin : Universitext. Springer-Verlag . (An introduction with applications)
  • M.I. Freidlin A.D. Wentzell. Random Perturbations of Dynamical Systems, Volume 260 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 2nd edn Springer-Verlag. New York. 1998 (Translated from the 1979 Russian original by Joseph Szücs).
  • Stone , E and Armbruster , D . 1999 . Noise and O(1) amplitude effects on heteroclinic cycles . Chaos , 9 ( 2 ) : 499
  • A. Katok and B. Hasselblatt. Introduction to the Modern Theory of Dynamical Systems, Volume 54, Encyclopedia of Mathematics and its Applications, Cambridge University Press, Cambridge, 1995 (With a supplementary chapter by Katok and Leonardo Mendoza).
  • Almada Monter , SA and Bakhtin , Y . Normal forms approach to diffusion near hyperbolic equilibria . (Submitted to Nonlinearity)
  • Billingsley , P . 1999 . “ Convergence of Probability Measures ” . In , Wiley Series in Probability and Statistics: Probability and Statistics, , 2nd , New York : John Wiley & Sons Inc. .

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